Extrapolation to the complete basis-set limit in density-functional theory using statistical learning

Speckhard DT, Carbogno C, Ghiringhelli LM, Lubeck S, Scheffler M, Draxl C (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Physical Review Materials American Physical Society

Book Volume: 9

Article Number: 013801

Journal Issue: 1

DOI: 10.1103/PhysRevMaterials.9.013801

Abstract

The numerical precision of density-functional-theory (DFT) calculations depends on a variety of computational parameters, one of the most critical being the basis-set size. The ultimate precision is reached in the limit of a complete basis set (CBS). Our aim in this work is to find a machine-learning model that extrapolates finite basis-size calculations to the CBS limit for periodic crystal structures. We start with a data set of 63 binary solids investigated with two all-electron DFT codes, exciting and FHI-aims, which employ very different types of basis sets. A quantile-random-forest model and a symbolic regression approach using the SISSO model are used to estimate the total-energy correction with respect to a fully converged calculation as a function of the basis-set size. The random-forest model achieves a symmetric mean absolute percentage error of lower than 25% for both codes and outperforms previous approaches in the literature. SISSO outperforms the random forest model for the exciting code. Our approach also provides prediction intervals, which quantify the uncertainty of the models' predictions.

Authors with CRIS profile

Luca Ghiringhelli

Involved external institutions

Fritz-Haber-Institut der Max-Planck-Gesellschaft (FHI) DE Germany (DE) Humboldt-Universität zu Berlin DE Germany (DE)

How to cite

APA:

Speckhard, D.T., Carbogno, C., Ghiringhelli, L.M., Lubeck, S., Scheffler, M., & Draxl, C. (2025). Extrapolation to the complete basis-set limit in density-functional theory using statistical learning. Physical Review Materials, 9(1). https://doi.org/10.1103/PhysRevMaterials.9.013801

MLA:

Speckhard, Daniel T., et al. "Extrapolation to the complete basis-set limit in density-functional theory using statistical learning." Physical Review Materials 9.1 (2025).

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